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Libby saved $100 in an account earning 2.5% compound interest. How much interest would her account earn in 20 years​

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Final answer:

The interest earned would be $58.986.

To find the interest earned, we subtract the principal amount (P) from the total amount (A):

Interest earned = $158.986 - $100 = $58.986

Step-by-step explanation:

To calculate the compound interest, we can use the formula A = P(1 + r/n)^(nt), where:

  • A is the total amount including interest
  • P is the principal amount (initial investment)
  • r is the annual interest rate (expressed as a decimal)
  • n is the number of times that interest is compounded per year
  • t is the number of years

In this case, Libby saved $100, so the principal amount (P) is $100. The interest rate (r) is 2.5% or 0.0256 as a decimal. The interest is compounded annually, so the number of times that interest is compounded per year (n) is 1. The time period (t) is 20 years.

Using the formula:

A = 100(1 + 0.0256/1)^(1 * 20)

A = 100(1.0256)^(20)

A = 100(1.5898581)

A = $158.986

To find the interest earned, we subtract the principal amount (P) from the total amount (A):

Interest earned = $158.986 - $100 = $58.986

User Gabriele Franco
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